Shumba hit Alasdair Evans for three consecutive sixes in a 17th over which brought 25 runs to turn the tide.
Scotland had been on track for victory when reducing Zimbabwe to 74 for three after 12 overs, after posting 177 for four.
But Shumba and Wesley Madhevere helped smash the tourists over the line with five balls left at The Grange.
The pair put on a partnership of 99 runs to reverse Zimbabwe’s momentum and put Scotland firmly on the back foot after Evans and Michael Leask had bowled Regis Chakabva, Craig Ervine and Sean Williams.
Madhevere was eventually run out in the 18th over but Shumba cracked another two fours to leave the visitors needing only two runs from the final over.
Scotland: 177/4 in 20 overs (Munsey 54)
Zimbabwe: 180/4 in 19.1 overs (Shumba 66 n.o). (BBC)